Problem: What do the following two equations represent? $-3x-2y = -4$ $6x+4y = 1$
Solution: Putting the first equation in $y = mx + b$ form gives: $-3x-2y = -4$ $-2y = 3x-4$ $y = -\dfrac{3}{2}x + 2$ Putting the second equation in $y = mx + b$ form gives: $6x+4y = 1$ $4y = -6x+1$ $y = -\dfrac{3}{2}x + \dfrac{1}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.